Varieties of Language Observed During a math lesson in a Traditional Classroom
Learning to talk “math” in a traditional fifth grade classroom in San Jose de Costa Rica
By Jessica Villegas
General Background: 5
Thesis/Central question: 5
Semiotic perspectives: 5
Socio-cultural theories of cognitive and linguistic development 6
Authoritative discourse vs. Internally persuasive discourse 6
Contextualized vs. De-contextualized learning 7
Discourse as scaffold 7
Zone of Proximal Development (ZPD) 8
Legitimate Peripheral Participation (LPP) 8
The Three Focal Aspects: 8
1. The practice of “Repaso” in a math lesson 8
2. The ubiquitous “minuend syndrome” 8
3. From group instruction to individual feedback, 9
Description of the field site 9
The school 9
The Classroom 9
The Teacher 10
The math lesson 11
Research Team 13
Division of labor 13
Consolidation of Data 14
Data Management 15
Data Matrix 15
Conceptual Map 16
A semiotic perspective on the practice of “Repaso” 20
The ubiquitous “minuend syndrome” 25
From group instruction to individual feedback 30
Group scaffolding through peer-to-peer teaching 32
Broadening constructionism’s dominions in the learning space 33
Conclusion: The tradition of learning to “talk math” 35
Literature Cited 37
Transcript of the Class 38
The importance of this ethnographic study stems from the need to investigate and document the transformations within the learning space at school as the practices of primary education and the local community are mediated through technologies, such as computers in Costa Rica.
In my ethnography I analyze the language of learning by applying the properties of semiotics to the various dimensions of classroom discourse within a traditional fifth grade class in Heredia, Costa Rica. Informing my analysis with education theory and the possible implications of digital technologies in classroom learning, I will reveal that semiotics elucidates the underlying framework of the activity of repaso, illuminating an entire practice within traditional “school math.”
The study of classroom discourse has been defined as “a kind of applied linguistics—the study of situated language use in one social setting.” (3) On account of this frame of reference, I found it appropriate to analyze and interpret my data in terms of semiotics. Additionally, the reasons for this focus emanate from data documented through passive and complete participant-observation of a mathematics lesson that captured different layers of discourse pertaining to the technical mathematical discourse register in addition to the colloquial usage of language to describe everyday activities.
By tracking a particular practice of the traditional classroom, one is more capable of understanding and guiding the course it will take in the nontraditional Classmate classroom and can thus guide this innovation of the 1:1 laptop initiative to improve the current framework underlying current classroom learning.
Within the 5th grade traditional classroom I observed, there is already an emerging constructionist attitude that is setting the path for a more efficient transition to a one-to-one learning environment that will transform the educational system in Costa Rica.
Because of a deeply rooted fascination and inquisitiveness for the nature of language and the meaning and implications behind its multitudinous manifestations in society, I was immediately absorbed with the classroom discourse the moment I entered a 5th grade traditional classroom in Heredia, Costa Rica. The boisterous students appeared to have control over the class, while the teacher stood in the front, attempting to introduce our small research team to them. However, once the lesson commenced, the teacher regained command of the classroom and I began to observe patterns in language usage in light of an ethnography by Catalina Laserna, 1988. In her ethnography, there is an extensive discourse analysis of a first grade math class in San Juan, Colombia that elucidates the emphasis on learning vocabulary over understanding the abstract concepts behind the terms. The review lesson of division I observed during the 5th grade math class in Costa Rica further illuminates this tradition of learning the vocabulary necessary to “talk math” in the classroom.
During my fieldwork I decided to focus on the teacher since I had the impression that the practice of learning the formal terminology was a tradition carried on by the teacher and foisted upon the students. Moreover, the following excerpt from British researcher, Douglas Barnes, attested to this impression:
Speech unites the cognitive and the social. The actual (as opposed to the intended) curriculum consists in the meanings enacted or realized by a particular teacher and class. In order to learn, students must use what they already know so as to give meaning to what the teacher presents to them. Speech makes available to reflection the processes by which they relate new knowledge to old. But this possibility depends on the social relationships, the communication system, which the teacher sets up. 1
In addition to focusing on the teacher’s diction and behavior in relation to the methodology of the activity of repaso, I found the math class a unique opportunity to make an actual contribution to the movement for innovation and improvement in the educational system in Costa Rica since: “Surprising as it may seem, mathematics is the subject area in which the current movement to change patterns of classroom discourse got its first and, arguably still most powerful push.”2
In Costa Rica, there has been a history of innovative ideas and strategies whose purpose is to further advance education via implementation of digital technologies. The digital technologies that are entering the classrooms of children are becoming a more dominant and crucial component of a student’s education. The Omar Dengo Foundation (FOD), which is a private, nonprofit organization created in 1987, has introduced digital technologies along with pedagogic theories of learning with the goal of educational innovation. The main objective of the FOD is to innovate the established educational processes by way of computer science and new technologies. Currently, there is one 5th grade class at Fidel Chaves in which every student has their own personal Classmate laptop. This One-to-One laptop initiative will be extended to other 5th grade classes at the school in the near future.